CN113946999B - Optimized simulation analysis method for improving heating uniformity of microwave oven - Google Patents
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Abstract
The invention discloses an optimized simulation analysis method for improving heating uniformity of a microwave oven, which comprises the steps of firstly, establishing a geometric model of the microwave oven; and defining a control equation and a boundary constraint equation in a geometric area, taking discrete boundary grid nodes as optimal design parameters, calculating updated node positions in a deformation area by using a motion grid equation, and repeatedly iterating to obtain boundary positions of the microwave oven to form a new microwave oven structure. And a partial differential equation of an electromagnetic field is solved by using a finite element method, and a temperature field is obtained by using a coupling heat transfer model, so that the feasibility of the method is verified. The method can lead the energy distribution of microwave heating to be more uniform, effectively avoid overheating effect in the process of heating food by microwaves, verify the feasibility of changing the shape and structure of the microwave oven to improve the heating uniformity, and provide reliable basis and effective data for further researching and developing the shape of the microwave oven.
Description
Technical Field
The invention belongs to the technical field of computer data processing, and particularly relates to a numerical optimization simulation analysis method for improving microwave field uniformity distribution of a microwave oven.
Background
With the development of social progress and microwave energy utilization technology, the use of microwave ovens is becoming more and more popular. Microwave heating is conducted through material energy dissipation, and then the medium is directly heated, so that the microwave heating has the advantages of high heating efficiency, high energy utilization rate, selective heating, environmental friendliness and the like, and by virtue of the advantages, microwaves are widely used for material processing in food engineering, chemical engineering and many other fields. However, microwave heating has certain defects, which limits the further application of the microwave oven, and most commonly, the heating is uneven, so that overripe and undercooked areas appear in the food, and the food cannot be safely eaten, thereby limiting the effective application of microwave energy. Therefore, the phenomenon of uneven temperature distribution of heated materials in the microwave heating process is significant.
One of the main causes of non-uniformity in heating of a microwave oven is due to non-uniformity in energy distribution of the microwave oven cavity. In order to improve the non-uniformity of the energy distribution in space, most of the existing solutions are methods using microwave field agitators and rotating turntables. The microwave field stirrer is generally composed of a plurality of metal fan blades coaxially arranged at the top of a microwave oven cavity, and the rotation of the metal fan blades can change the boundary condition of the microwave oven cavity under the drive of a motor, so that the electromagnetic field distribution in the microwave oven rotates or continuously changes along with the rotation of the blades, and the uniformity of a microwave field can be improved to a certain extent. However, the moving metal elements used by the stirrer and the rotary table require a lot of resources for mass production. In order to overcome the defects of the prior art, the shape and the structure of the microwave oven need to be fundamentally changed, so that the defect of uneven energy distribution in the microwave oven is overcome.
Disclosure of Invention
Aiming at the current situation that the heating in the microwave oven is uneven and an effective and feasible shape optimization simulation technology is lacked, the invention provides an optimization simulation analysis method for improving the heating uniformity of the microwave oven, and an arbitrary Lagrange Euler method is applied to the shape optimization of the microwave oven so as to improve the condition of uneven energy distribution in a microwave cavity.
The invention provides an optimized simulation analysis method for improving heating uniformity of a microwave oven, which comprises the following steps:
(1) Establishing a finite element model of a microwave oven
Drawing a two-dimensional initial geometric model of the microwave oven in finite element analysis software, wherein the two-dimensional initial geometric model comprises a waveguide, a microwave cavity, a heating disc and a heated object, defining and determining electromagnetic characteristic parameters of the heated object, the heating disc and medium air in the microwave cavity, and performing grid division on the built initial geometric model of the microwave oven;
(2) Control equation for defining microwave oven geometric model grid area
Wherein E is the electric field strength, k 0 Free space wave,μ r Is relative permeability epsilon r For relative permittivity epsilon 0 Is the dielectric constant in vacuum, σ is the conductivity, ω is the angular frequency, j is the imaginary number; by solving the maxwell Wei Bodong equation, the electric field distribution in the microwave cavity can be obtained.
(3) Defining objective functions and constraints for shape optimization
s.t.：-d max ≤d≤d max
Wherein Q is e Represents the absorption power density of the heated object, Ω represents the optimizable area, d represents the boundary grid movement displacement, Q ei Representing the absorbed power density of each region of the heated object;representing the average absorbed power density of the heated object; covariance COV is used to describe the uniformity of heating;
taking COV as an objective function, optimizing and solving the minimum value of the COV, and carrying out operation by adopting a mobile asymptote method (MMA) solver;
(4) Solving and optimizing electromagnetic field distribution in microwave oven
Initializing, namely initializing the finite element model of the microwave oven obtained in the step (1), and taking discrete boundary grid nodes as optimization design parameters, wherein the positions of the boundary grid nodes need to be continuously updated in the optimization process;
(4.2) calculating electromagnetic field distribution, and solving the control equation in the step (2) by using a finite element method to obtain the electromagnetic field distribution of the current iteration microwave cavity;
(4.3) judging whether the set optimization target or the maximum iteration number is reached, if so, obtaining the boundary position of the microwave oven, and completing the task; if the initial value is not reached, increasing the iteration times on the basis of the current boundary grid, and continuing the following steps as the initial value of the next optimization;
(4.4) grid movement, on the basis of the current microwave cavity boundary grid node displacement, calculating the updated grid node position in the design domain by using a motion grid equation with a normal speed boundary condition, acquiring a new grid node displacement value, loading the new grid node displacement value on a grid, completing grid movement, and repeating the step (4.2).
In the above method, further, the principle of meshing the initial geometric model of the microwave oven in the step (1) is that the mesh size is not greater than one sixth of the working wavelength. For a two-dimensional geometric model, the cells resulting from meshing are typically triangular cells or quadrilateral cells, and the mesh can be properly encrypted by setting the maximum mesh size at the heated object.
In the method, further, in the step (1), COMSOL Multiphysics software is adopted to perform simulation calculation of the two-dimensional initial geometric model of the microwave oven.
In the above method, further, in step (4.4), the ALE module in COMSOL Multiphysics is adopted to perform grid movement setting, that is, the grid movement is completed by adopting any lagrangian euler method.
In the above method, further, the quality of the grid may be reduced due to the deformation of the design domain in the optimization process. In order to improve the grid quality of the design domain, in the step (4.4), an updated grid node position in the design domain is calculated by adopting a Laplace smoothing method; in each iteration process of shape optimization, a displacement filtering method is adopted to improve the non-smoothness of the free deformation boundary, and a Helmholtz partial differential equation filter which is easy to realize by finite element software and has high filtering calculation efficiency is preferably adopted.
The invention also provides a method for verifying the microwave heating uniformity improvement of the method, which comprises the following steps:
obtaining electric field distribution in the microwave cavity and the heated object by solving maxwell electromagnetic equation, and obtaining temperature by coupling heat transfer model; the thermal process of microwave heating is determined by the heat transfer equation.
Wherein T is the temperature; ρ is the density; c (C) p Is a heat capacity; k is the heat transfer coefficient; the heated object boundary is considered an insulating boundary.
Compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, the random Lagrangian Euler method is applied to the shape optimization of the microwave oven, and through verification, the condition of uneven energy distribution in the microwave cavity can be effectively improved, and uneven heating is avoided, so that the overheating effect in the process of heating food by microwaves is avoided.
2. The method has universality for optimizing the shapes of various microwave devices, and can also be applied to directional heating of microwave chemical reactors, microwave plasma devices and the like.
Drawings
FIG. 1 is a schematic diagram of a two-dimensional initial geometric model of a microwave oven;
FIG. 2 is a grid diagram (left is an initial model, right is a final model obtained by optimization) obtained by grid division of an initial geometric model of a microwave oven;
FIG. 3 is a relationship between the iteration number and the COV value of the objective function in the solution process;
FIG. 4 is a graph showing the electric field modulus distribution for each iteration;
FIG. 5 is a graph comparing geometric boundaries of an initial model and an optimized model;
FIG. 6 is a graph showing the temperature distribution of the potato surface at various times;
FIG. 7 is a graph of covariance of temperature versus heating time.
Detailed Description
The following describes the optimized simulation analysis method for improving the heating uniformity of the microwave oven according to the present invention by means of a specific embodiment.
Example 1
According to the optimized simulation analysis method for improving the heating uniformity of the microwave oven, the shape structure of the microwave oven is calculated and analyzed through a numerical simulation method, and then the shape boundary of the microwave oven cavity is reconstructed through a grid moving method, so that the boundary distribution related parameters of the microwave cavity are obtained, and further a new microwave oven structure is obtained. In the optimization process, discrete boundary grid nodes are used as optimization design parameters, and the grid node positions of the boundaries are required to be continuously updated in the optimization process. Since only the movement speed of the boundary node is defined in the optimization analysis, the movement of the grid node in the structural region needs to be additionally defined in order to ensure the coordination of the whole discrete grid of the structure. Therefore, adjusting or even repartitioning the mesh during the design process is an important step in shape optimization. The mobile grid method is a dynamic grid adjustment method, and the numerical implementation is based on a mobile grid partial differential equation. The change in the structure boundaries is accommodated by the movement of the mesh nodes, with the mesh topology remaining unchanged. The mobile grid method is complex, and the numerical implementation difficulty is higher. In order to ensure stability of numerical solution, a high-precision transient solver is required, and the ALE module in COMSOL Multiphysics is adopted to solve the problem.
The method comprises the following steps:
(1) Establishing a finite element model of the microwave oven, which comprises the following steps of:
(1.1) a two-dimensional initial geometric model of the microwave oven is drawn in finite element analysis software COMSOL Multiphysics, as shown in fig. 1, and comprises four parts, namely a waveguide, a microwave cavity, a glass plate and a potato chip as a heated object. The potato chip and the glass disk are placed in the center of the cavity, and the waveguide is positioned on the left side of the cavity. The geometric origin (0, 0) is the right center of the microwave cavity, the glass disk and the potato slices, the size of the potato slices is 5cm multiplied by 4cm, the radius of the glass disk is 7cm, the side length of the microwave cavity is 40cm multiplied by 38cm, the size of the rectangular waveguide is 10.9cm multiplied by 5cm in the middle of the left side of the microwave cavity, and the leftmost side is the waveguide feed port.
(1.2) defines the electromagnetic properties of the potato flakes, glass disk, and the medium air in the microwave cavity, the parameters of which are shown in Table 1. Wherein the relative dielectric constant of the potato slices is set by considering the influence of temperature on the dielectric constant in the heating process.
Table 1: magnetic property parameter of model material
(1.3) mesh-dividing the initial geometric model of the microwave oven, dividing the potato chip portion of the heating target by using a free triangular mesh with a maximum cell size of 2[ mm ], dividing the remaining geometric portion in FIG. 1 by using a triangle with a maximum cell size of 16[ mm ] and a minimum cell size of 0.0563[ mm ], and obtaining the mesh as shown in the left initial model of FIG. 2.
(2) Control equation for defining microwave oven geometric model grid area according to Helmholtz equation
Wherein E is the electric field strength, k 0 Wavenumber, k of free space 0 2 ＝ω 2 μ 0 ε 0 ，μ r Is relative permeability epsilon r For relative permittivity epsilon 0 Is the dielectric constant in vacuum, σ is the conductivity, ω is the angular frequency, j is the imaginary number
In this embodiment, the port excitation electromagnetic wave is TE 10 The wave has a frequency of 2.45GHz and a power of 300W.
(3) Shape optimized objective function and constraints
Covariance COV is used to describe the uniformity of heating, with smaller COV values, the more uniform the temperature distribution of the potato during heating.
s.t.：-d max ≤d≤d max
In which Q e Representing the absorbed power density of the potato, Ω represents the optimizable area, d represents the edgeThe world wide web moves by displacement.
In this embodiment, the two end points of the waveguide are set as fixed points, the four walls of the microwave cavity are set as free-form boundaries, and the domain inside the cavity is set as a free-form domain. COV is used as an objective function, and the minimum value of the COV is optimized and solved. And in the optimization process, a mobile asymptote method (MMA) solver is adopted for operation. The solver is universal, is constructed according to gradient information of objects and constraints based on an interior point method of continuous convex approximation, and is particularly suitable for the shape optimization problems such as topology and the like.
(4) Solving and optimizing electromagnetic field distribution in a microwave oven, comprising the following sub-steps:
initializing, namely initializing the finite element model of the microwave oven obtained in the step (1), and taking discrete boundary grid nodes as optimization design parameters, wherein the positions of the boundary grid nodes need to be continuously updated in the optimization process;
(4.2) calculating electromagnetic field distribution, and solving a control equation by using a finite element method to obtain the electromagnetic field distribution of the current iteration microwave cavity;
(4.3) judging whether the set optimization target or the maximum iteration number is reached, if so, obtaining the boundary position of the microwave oven, and completing the task; if the initial value is not reached, increasing the iteration times on the basis of the current boundary grid, and continuing the following steps as the initial value of the next optimization;
(4.4) in COMSOL Multiphysics the ALE module performs a grid movement setup, introducing any Lagrangian Euler method into shape optimization. In order to improve the grid quality of the design domain, the updated grid node position in the design domain is calculated by using a motion grid equation Laplacian smoothing method with normal speed boundary conditions on the basis of the current microwave cavity boundary grid node displacement, a new grid node displacement value is obtained and loaded on the grid, and grid movement is completed; in each iteration process of shape optimization, a Helmholtz partial differential equation filter is adopted to improve the non-smoothness of the free deformation boundary; the step (4.2) is repeated.
When the maximum variation of the design variable between iterations is less than a certain value, then the optimization process is convergent. Two criteria are used to stop the loop optimization process, one is the optimization tolerance and the other is the maximum number of iterations. In this embodiment, the optimization tolerance is set to 0.001, and the maximum number of iterations is set to 30. The relationship between the iteration number and the COV value of the objective function in the solving process is shown in fig. 3. As can be seen from the figure, the optimizing method effectively improves the non-uniformity in the heating process of the microwave oven. The electric field modulus profile for each iteration is plotted in fig. 4, which shows that the electric field distribution around the potato is gradually uniform with increasing number of iterations. The grid diagram of the final model obtained by optimization is shown on the right side of fig. 2, and the geometric boundary contrast diagram of the initial model and the optimized model is shown in fig. 5.
The optimized cavity shape of the microwave oven is used for heating, whether uniformity is improved is demonstrated, electric field distribution in the microwave oven and the food is obtained by solving maxwell electromagnetic equation, and temperature is obtained by a coupling heat transfer model. The calculation of the heating process was performed using the following heat transfer equation.
Wherein T is the temperature; ρ is the density; c (C) p Is a heat capacity; t is the heating time; k is the heat transfer coefficient; q (Q) e (t) is a heat source. The boundaries of the potatoes are considered as insulating boundaries.
The initial temperature in this example was set at 20C and the heating time was set at 20s. The initial model and the optimized model are respectively subjected to simulation of a heating physical field, and the temperature distribution of the potato surface at different moments is shown in fig. 6. A graph of temperature covariance versus heating time is shown in fig. 7. And comparing the initial model and the optimized model in the two graphs, and greatly improving the uniformity of the optimized model. This demonstrates the reliability and practicality of the method.
Through the optimized simulation analysis, the arbitrary Lagrangian Euler method is applied to changing the shape of the microwave oven, so that the energy distribution is more uniform, and the overheating effect in the process of heating food by microwaves can be effectively avoided, thereby verifying the feasibility of changing the shape and structure of the microwave oven to improve the heating uniformity and providing reliable basis and effective data for further researching and developing the shape of the microwave oven.
Those of ordinary skill in the art will recognize that the embodiments herein are intended to assist the reader in understanding the principles of the invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (7)
1. An optimized simulation analysis method for improving heating uniformity of a microwave oven is characterized by comprising the following steps:
(1) Establishing a finite element model of a microwave oven
Drawing a two-dimensional initial geometric model of the microwave oven in finite element analysis software, wherein the two-dimensional initial geometric model comprises a waveguide, a microwave cavity, a heating disc and a heated object, defining and determining electromagnetic characteristic parameters of the heated object, the heating disc and medium air in the microwave cavity, and performing grid division on the built initial geometric model of the microwave oven;
(2) Control equation for defining microwave oven geometric model grid area
Wherein E is the electric field strength, k 0 Free space wave,μ r Is relative permeability epsilon r Is the relative mediumElectric constant, epsilon 0 Is the dielectric constant in vacuum, σ is the conductivity, ω is the angular frequency, j is the imaginary number; by solving the Maxwell Wei Bodong equation, the electric field distribution in the microwave cavity can be obtained;
(3) Defining objective functions and constraints for shape optimization
s.t.:-d max ≤d≤d max
Wherein Q is e Represents the absorption power density of the heated object, Ω represents the optimizable area, d represents the boundary grid movement displacement, Q ei Representing the absorbed power density of each region of the heated object;representing the average absorbed power density of the heated object; covariance COV is used to describe the uniformity of heating; taking COV as an objective function, optimizing and solving the minimum value of the COV, and carrying out operation by adopting a mobile asymptote method (MMA) solver;
(4) Solving and optimizing electromagnetic field distribution in microwave oven
Initializing, namely initializing the finite element model of the microwave oven obtained in the step (1), and taking discrete boundary grid nodes as optimization design parameters, wherein the positions of the boundary grid nodes need to be continuously updated in the optimization process;
(4.2) calculating electromagnetic field distribution, and solving the control equation in the step (2) by using a finite element method to obtain the electromagnetic field distribution of the current iteration microwave cavity;
(4.3) judging whether the set optimization target or the maximum iteration number is reached, if so, obtaining the boundary position of the microwave oven, and completing the task; if the initial value is not reached, increasing the iteration times on the basis of the current boundary grid, and continuing the following steps as the initial value of the next optimization;
(4.4) grid movement, on the basis of the current microwave cavity boundary grid node displacement, calculating the updated grid node position in the design domain by using a motion grid equation with a normal speed boundary condition, acquiring a new grid node displacement value, loading the new grid node displacement value on a grid, completing grid movement, and repeating the step (4.2).
2. The method of claim 1, wherein the meshing of the initial geometric model of the microwave oven established in step (1) is based on a meshing size of not more than one sixth of the operating wavelength.
3. A method according to claim 2, characterized in that the mesh cells obtained by the meshing are triangular cells or quadrangular cells, the mesh being suitably encrypted by setting the maximum mesh size at the heating object.
4. The method of claim 1, wherein step (1) uses COMSOL Multiphysics software to perform a simulation calculation of the two-dimensional initial geometric model of the microwave oven.
5. The method of claim 1, wherein the step (4.4) uses the ALE module in COMSOL Multiphysics to perform the grid movement, i.e., uses any lagrangian euler method to perform the grid movement.
6. The method of claim 1, wherein the step (4.4) uses laplacian smoothing to calculate updated mesh node locations within the design domain; in each iteration of shape optimization, a displacement filtering method is adopted to improve the non-smoothness of the free deformation boundary.
7. The method of claim 6, wherein step (4.4) employs a helmholtz partial differential equation filter that is easily implemented in finite element software and has high filtering computational efficiency during each iteration of shape optimization to improve the non-smoothness of the free deformation boundary.
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